Matching of Shapes Bound by Freeform Curves

References

• Ankerst, M.; Kastenmueller, G.; Kriegel, H.-P.; Seidl, T.: 3d shape histograms for similarity search and classification in spatial databases. In SSD ’99: Proceedings of the 6th International Symposium on Advances in Spatial Databases, London, UK, 1999. Springer-Verlag, 207–226.
   Google Scholar
• Belkin, M.; Niyogi, P.: Laplacian eigenmaps for dimensionality reduction and data representation. Neural Comput., 15(6), 2003, 1373–1396, doi: 10.1162/089976603321780317
   Web of Science ®Google Scholar
• Biasotti, S.; Giorgi, D.; Spagnuolo, M.; Falcidieno, B.: Reeb graphs for shape analysis and applications. Theor. Comput. Sci., 392(1-3), 2008, 5–22. doi: 10.1016/j.tcs.2007.10.018
   Web of Science ®Google Scholar
• Blum, H.: A transformation for extracting new descriptors of shape. Models for the Perception of Speech and Visual Form, 1967, 362–381.
   Google Scholar
• Blum, H.; Nagel, R. N.: Shape description using weighted symmetric axis features, Pattern Recognition, 10, 1978, 167–180, doi: 10.1016/0031-3203(78)90025-0
   Web of Science ®Google Scholar
• Cao, L.; Liu, J.: Computation of medial axis and offset curves of curved boundaries in planar domain. Comput. Aided Des., 40(4), 2008, 465–475. doi: 10.1016/j.cad.2008.01.002
   Web of Science ®Google Scholar
• Chen, D.-Y.; Ouhyoung, M.; Tian, X.-P.; Shen, Y.-T.; Ouhyoung, M.: On visual similarity based 3d model retrieval. Euro graphics, Granada, Spain, 2003, 223–232.
   Google Scholar
• Cohen, S.; Elber, G.; Bar-Yehuda, R.: Matching of freeform curves, Computer-Aided Design, 29(5), 1997, 369–378, doi: 10.1016/S0010-4485(96)00075-9
   Web of Science ®Google Scholar
• Coifman, R. R.; Lafon, S.; Lee, A. B.; Maggioni, M.; Nadler, B.; Warner, F.; Zucker, S. W.: Geometric diffusions as a tool for harmonic analysis and structure definition of data: Diffusion maps. Proceedings of the National Academy of Sciences, 102(21), May 2005, 7426–7431. doi: 10.1073/pnas.0500334102
   PubMed Web of Science ®Google Scholar
• Cui, M.; Femiani, J.; Hu, J.; Wonka, P.; Razdan, A.: Curve matching for open 2d curves. Pattern Recognition Letters, 30(1), 2009, 1 – 10.
   Web of Science ®Google Scholar
• Cybenko, G.; Bhasin, A.; Cohen, K. D.: Pattern recognition of 3D CAD objects: Towards an electronic yellow pages of mechanical parts, Smart Engineering Systems Design, 1, 1997, 1–13.
   Google Scholar
• Elad, A.; Kimmel, R.: On bending invariant signatures for surfaces, IEEE Transactions on Pattern Analysis and Machine Intelligence, 25(10), October 2003, 1285–1295. doi: 10.1109/TPAMI.2003.1233902
   Web of Science ®Google Scholar
• Fudos, I.; Palios, L.: An efficient shape-based approach to image retrieval, Pattern Recognition Letters, 23(6), 2002, 731 – 741.
   Web of Science ®Google Scholar
• Funkhouser, T.; Shilane P.: Partial matching of 3d shapes with priority-driven search. In SGP ’06: Proceedings of the fourth Eurographics symposium on Geometry processing, Aire-la-Ville, Switzerland, Switzerland, 2006. Eurographics Association, 131–142.
   Google Scholar
• Gal, R.; Cohen-Or, D.: Salient geometric features for partial shape matching and similarity. ACM Trans. Graph., 25(1), 2006, 130–150. doi: 10.1145/1122501.1122507
   Web of Science ®Google Scholar
• Gal, R.; Shamir, A.; Cohen-Or, D.: Pose-oblivious shape signature, IEEE Transactions on Visualization and Computer Graphics, 13(2), Mar./Apr. 2007, 261–271. doi: 10.1109/TVCG.2007.45
   PubMed Web of Science ®Google Scholar
• Goh, W.-B.: Strategies for shape matching using skeletons, Comput. Vis. Image Underst., 110(3), 2008, 326–345. doi: 10.1016/j.cviu.2007.09.013
   Web of Science ®Google Scholar
• Hanniel, I.; Muthu ganapathy, R.; Elber, G.; Kim M.-S.,: Precise voronoi cell extraction of free-form rational planar closed curves. In SPM ’05: Proceedings of the 2005 ACM symposium on Solid and physical modeling, New York, NY, USA, 2005. ACM, 51–59.
   Google Scholar
• Hilaga, M.; Shinagawa, Y.; Kohmura, T.; Kunii, T. L.: Topology matching for fully automatic similarity estimation of 3d shapes. In SIGGRAPH ’01: Proceedings of the 28th annual conference on Computer graphics and interactive techniques, New York, NY, USA, 2001. ACM, 203–212.
   Google Scholar
• Iyer, N.; Jayanti, S.; Lou, K.; Kalyanaraman, Y.; Ramani, K.: Three-dimensional shape searching: state-of-the-art review and future trends, Computer-Aided Design, 37(5), 2005, 509–530. doi: 10.1016/j.cad.2004.07.002
   Web of Science ®Google Scholar
• Jain, A.; Muthu ganapathy, R.; Ramani, K. Content-based image retrieval using shape and depth from an engineering database, In International Symposium on Visual Computing (2), 2007, 255–264.
   Google Scholar
• Jain, V.; Zhang, H.: A spectral approach to shape-based retrieval of articulated 3d models. Comput. Aided Des., 39(5) 2007, 398–407. doi: 10.1016/j.cad.2007.02.009
   Web of Science ®Google Scholar
• Jayanti, S.; Kalyanaraman, Y.; Iyer, N.; Ramani, K.: Developing an engineering shape benchmark for cad models, Computer-Aided Design, 38(9), 2006, 939–953. doi: 10.1016/j.cad.2006.06.007
   Web of Science ®Google Scholar
• Joachim, T. D.; Giesen, J.; Goswami, S.: Shape segmentation and matching with flow discretization. In Proc. Workshop on Algorithms and Data Structures, 2003, 25–36.
   Google Scholar
• Kim, D.-S.; Hwang, I.-K.; Park, B.-J.: Representing the voronoi diagram of a simple polygon using rational quadratic Bezier curves, Computer-Aided Design, 27(8), 1995, 605–614. doi: 10.1016/0010-4485(95)99797-C
   Web of Science ®Google Scholar
• Kriegel, H.-P.; Kroeger, P.; Mashael, Z.; Pfeifle, M.; Pötke, M.; Seidl, T.: Effective similarity search on voxelized cad objects. In DASFAA ’03: Proceedings of the Eighth International Conference on Database Systems for Advanced Applications, Washington, DC, USA, 2003. 27.
   Google Scholar
• Latecki, L. J.; Lakmper R.; Eckhardt U.: Shape descriptors for non-rigid shapes with a single closed contour. In Proc. IEEE Conf. Computer Vision and Pattern Recognition, 2000, 424–429.
   Google Scholar
• Levy B.: Laplace-beltrami eigen functions towards an algorithm that ”understands” geometry. In SMI ’06: Proceedings of the IEEE International Conference on Shape Modeling and Applications, 2006, 13, Washington, DC, USA, 2006, IEEE Computer Society.
   Google Scholar
• Ling, H.; Jacobs, D. W.: Shape classification using the inner-distance, IEEE Trans. Pattern Anal. Mach. Intell, 29, 2007, 286–299.
   PubMed Web of Science ®Google Scholar
• McNeill, G.; Vijayakumar, S. : 2d shape classification and retrieval. In Proceedings of the 19th international joint conference on Artificial intelligence, San Francisco, CA, USA, 2005. Morgan Kaufmann Publishers Inc, 1483–1488.
   Google Scholar
• Nasreddine, K.; Benzinou, A.; Fablet, R.: Variational shape matching for shape classification and retrieval, Pattern Recognition Letters, 31(12), 2010, 1650–1657.
   Web of Science ®Google Scholar
• Ohbuchi, R.; Minamitani, T.; Takei, T.: Shape-similarity search of 3d models by using enhanced shape functions, In TPCG ’03: Proceedings of the Theory and Practice of Computer Graphics 2003, page 97, Washington, DC, USA, 2003, IEEE Computer Society.
   Google Scholar
• Ohbuchi, R.; Nakazawa, M.; Takei, T.: Retrieving 3d shapes based on their appearance. In MIR ’03: Proceedings of the 5th ACM SIGMM international workshop on Multimedia information retrieval, New York, NY, USA, 2003. ACM, 39–45.
   Google Scholar
• Osada, R.; Funkhouser, T.; Chazelle, B.; and Dobkin, D.: Shape distributions, ACM Trans. Graph., 21(4), 2002, 807–832. doi: 10.1145/571647.571648
   Web of Science ®Google Scholar
• Ramanathan, M.; Gurumoorthy, B.: Constructing medial axis transform of planar domains with curved boundaries, Computer-Aided Design, 35(7), June 2003, 619–632.
   Web of Science ®Google Scholar
• Rea, H. J.; Corney, J. R.; Clark, D. E. R.; Pritchard, J.; Breaks, M. L.; Macleod, R. A.: Part-sourcing in a Global Market, Concurrent Engineering, 10(4), 2002, 325–333, doi: 10.1177/106329302129140214
   Web of Science ®Google Scholar
• Rustamov, R. M.: Laplace-beltrami eigen functions for deformation invariant shape representation. In SGP ’07: Proceedings of the fifth Eurographics symposium on Geometry processing, Airela-Ville, Switzerland, Switzerland, 2007. Eurographics Association, 225–233.
   Google Scholar
• Saupe, D.; Vranic D. V.: 3d model retrieval with spherical harmonics and moments, In Proceedings of the 23rd DAGM-Symposium on Pattern Recognition, London, UK, 2001. Springer-Verlag, 392–397.
   Google Scholar
• Sebastian, T.; Klein, P.; Kimia, B. Recognition of shapes by editing their shock graphs Pattern Analysis and Machine Intelligence, , IEEE Transactions on, 26(5), May 2004, 550–571.
   Google Scholar
• Sebastian, T. B.; Klein, P. N.; Kimia, B. B.: Alignment-based recognition of shape outlines, In IWVF-4: Proceedings of the 4th International Workshop on Visual Form, London, UK, 2001. Springer-Verlag, 606–618.
   Google Scholar
• Sharvit, D.; Chan, J.; Tek, H.; Kimia, B. B.: Symmetry-based indexing of image databases, J. Visual Communication and Image Representation, 9, 1998, 366–380. doi: 10.1006/jvci.1998.0396
   Web of Science ®Google Scholar
• Shilane, P.; Min, P.; Kazhdan, M.; Funkhouser T.: The princeton shape benchmark, In Shape Modeling International, June 2004.
   Google Scholar
• Siddiqi, K.; Shokoufandeh, A.; Dickinson, S. J.; Zucker, S. W.: Shock graphs and shape matching. In ICCV, 1998, 222–229.
   Google Scholar
• Sundar, H.; Silver, D.; Gagvani, N.; Dickinson, S.: Skeleton based shape matching and retrieval. In SMI ’03: Proceedings of the Shape Modeling International, 2003, 290, Washington, DC, USA, 2003, IEEE Computer Society.
   Google Scholar
• Tangelder, J.; Veltkamp, R.: A survey of content based 3D shape retrieval methods. In SMI ’04: Proceedings of the Shape Modeling International, Washington, DC, USA, 2004, 145–156.
   Google Scholar
• Veltkamp, R.: Shrec home page. http://www.aimatshape.net/event/SHREC, 2010.
   Google Scholar
• Wolter, F. E.; Friese, K. I.: Local and global methods for analysis interogation, reconstruction, modification and design of shape, In Proceedings of Computer Graphics International Conference, Geneva, Switzerland, 2000. ACM, 137–151.
   Google Scholar
• Xie, J.; Heng, P.-A.; Shah, M.: Shape matching and modeling using skeletal context, Pattern Recogn., 41(5), 2008, 1756–1767. doi: 10.1016/j.patcog.2007.11.005
   Web of Science ®Google Scholar